A coffee tamper is a handheld device used to evenly distribute and compact the espresso grounds in the filter basket into a puck. This increases density and ensures that there are no voids in the coffee where water might find a path of least resistance.
When you decide to get a tamper the most important aspect is that the size fits the basket of your espresso maker. The diameters of filter baskets vary from 40 to 60mmm, the most common sizes are 52mm and 58mm.
A tamper should have a certain weight as it makes it easier to tamp.
Tampers can have a convex or a flat tamping surface. This is more a matter of preference like the material and the length of the handle. The criteria is it has to fit your taste!